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Table 6 Notation used for the Swissmod model

From: The future of Swiss hydropower: how to distribute the risk and the profits?

Indices/sets Parameters
\(n \in N\) Power nodes mc Marginal cost
\(l \in L\) Power lines d Demand
\(t \in T\) Time periods (hours) res Renewables in-feed
\({\mathrm{cp}} \in {\mathrm{CP}}\) Conventional power plants \({\eta }_{\mathrm{hp}}^{\mathrm{Turb}}\) Production equivalent [MWh/1000 m3]
\({\mathrm{hp}} \in {\mathrm{HP}}\) Hydropower plants \(\eta _{{{\mathrm{hp}}}}^{{{\mathrm{Pump}}}}\) Pumping efficiency factor
\({\mathrm{wn}},\overline{{\mathrm{wn}}},\underline{{\mathrm{wn}}} \in WN\) Water nodes CH (above, below) \(\eta _{{{\mathrm{hp}}}}^{{{\mathrm{rt}}}}\) Pumping round-trip efficiency
\({\mathrm{co}}\in \mathrm{CO}\) Countries inj Natural inflow to water node [1000 m3]
Matrices   chp Combined heat and power
\({\mathrm{inc}}_{n,l}\) Power grid incidence  {0,1, − 1} \({g}_{\mathrm{cp}}^{\mathrm{max}}\) Generation capacity
Variables   \({turb}_{\mathrm{hp}}^{\mathrm{max}}\) Turbine capacity [MW]
G Electricity generation \({pump}_{\mathrm{hp}}^{\mathrm{max}}\) Pump capacity [MW]
Turb Discharge (in water for CH, in electricity for EU) avail Availability conventional power plants
Pump Pumping (in water for CH, in electricity for EU) \({s}^{\mathrm{max}}\) Storage capacity [MW for EU, 1000 m3 for CH]
Cur Curtailment of renewables \({\mathrm{{turb}}}_{\mathrm{hp},t}^{\mathrm{profile}}\) Run-of-river profile (for EU)
F Line flow \({\mathrm{{turb}}}_{\mathrm{hp}}^{year}\) Dam generation per year (for EU)
S Storage level \({\mathrm{{susceptance}}}_{l}\) Line susceptance
WI Water inflow voltbase Line voltage base
WO Water outflow \({f}_{l}^{\mathrm{max}}\) Line capacity
Spill Spillage securitymargin Line security margin
Transfer Water transferred to other water node (without turbining or pumping)   
X Phase angle difference